Stupid word problem.?

Question

A telemarketing service uses a master computer to set up a chain of activating computers. The master computer links two computer and activates them. Then the activated computers each link with two other computers to activate them. At each step, the activation process takes 10 minutes. After an hour, how many computers have been activated?

This is what I got, but I think I'm wrong.


S sub 6 = 1 ( 1 - 2 ^ 6 / 1 - 2 )

S sub 6 = 1 ( 1 - 64 / -1 )

S sub 6 = -63/ -1

S sub 6 = 63

So, 63 computers, but would I count the first, activating computer?

I don't know whether to make the sequence

1+2+4+8+16+32

or

2+4+8+16+32+64

If it's the latter, the sum is 126, not 63.

Answer 1

I'm getting 126.
after
10 mins --------- 2
20 mins --------- 4
30 mins --------- 8
40 mins --------- 16
50 mins --------- 32
60 mins --------- 64
Total --------------126

The question really comes down to whether we should or should not include the 60th minute. If it takes exactly 10 mins, then the end of the 60th minute signifies the end of the hour, so it should be included.

Answer 2

Divide the hour by 10 minutes we will get 6 activation process.

The activation process is a binary tree in which each node is linked to two other nodes like this:


1 -> 2 -> 4 -> 8 -> etc

So in step n we have (n-1)*2 links activated where n ≥ 2 and in n = 1 we have 1 link activated. So 6-1 = 5 and we will calculate n for 2 to 5 like this:

n1 = 1
n2 = (1) * 2 = 2
n3 = (2) * 2 = 4
n4 = (4) * 2 = 8
n5 = (8) * 2 = 16
n6 = (16) * 2 = 32

Now add all Ns we will get

1+2+4+8+16 = 31

Note that this answer is wrong since the first computer did NOT take 10 minutes to be activated. Therefore, we need to calculate the sum of:

n2 + n3+ n4 + n5 + n6 + n7

n7 = (n6) * 2 = 32*2 = 64

n2 + n3+ n4 + n5 + n6 + n7 = 2 + 4 + 8 + 16 + 32 + 64 = 126

Therefore 126 links will be activated after 1 hour.

Good luck.

Answer 3

If you dont use the first computer as active then the answer is 63 if you do then it is 64 if it was me i would go with the 63 and not count the Master computer

Answer 4

126 according to your description, but I would double check that the first computer doesn't start activating two more computers after 10 minutes.

Answer 5

Computer 1 is not activated.
The activation sequence is 2,4,8,16,32,64
The sum is 126.